- 在线时间
- 5024 小时
- 最后登录
- 2022-11-28
- 注册时间
- 2009-4-8
- 听众数
- 737
- 收听数
- 1
- 能力
- 23 分
- 体力
- 76272 点
- 威望
- 96 点
- 阅读权限
- 255
- 积分
- 26808
- 相册
- 1
- 日志
- 14
- 记录
- 36
- 帖子
- 4293
- 主题
- 1341
- 精华
- 15
- 分享
- 16
- 好友
- 1975
数学中国总编辑
TA的每日心情 | 衰 2016-11-18 10:46 |
---|
签到天数: 206 天 [LV.7]常住居民III 超级版主
群组: 2011年第一期数学建模 群组: 第一期sas基础实训课堂 群组: 第二届数模基础实训 群组: 2012第二期MCM/ICM优秀 群组: MCM优秀论文解析专题 |
2#
发表于 2011-11-28 10:48
|只看该作者
|
|邮箱已经成功绑定
matlab下面的kalman滤波程序% e+ C" ~1 l7 @: v4 Y' C2 s
clear N=200; w(1)=0;
7 ?- O7 f3 B( {/ H tw=randn(1,N) + _9 F5 W! ~5 }/ C
x(1)=0; 3 z( z8 k- ~$ E9 H6 u) L) a
a=1; 9 M* n, I% O( b4 A" {
for k=2:N;
) Z* U* m! Q! I5 X& F* W7 Ux(k)=a*x(k-1)+w(k-1);
# q b% c8 V4 b, T7 W( E) Bend
5 g) f% [5 X/ K" X. FV=randn(1,N); & a% |% p" i/ r' r1 [; F( E
q1=std(V); & T3 P1 p/ d5 j
Rvv=q1.^2;
, U7 O8 G* ?+ ^( w# ?q2=std(x); 0 Y F* M# U9 `
Rxx=q2.^2;
( P) t0 z+ w" Xq3=std(w); 0 I* z! }* G% h' i% @ _
Rww=q3.^2; 2 l5 I8 _3 q0 V2 H$ R2 d
c=0.2;
! _6 B0 c1 k0 \Y=c*x+V;
) U# e8 V8 e( K) s% d& B9 ~6 Gp(1)=0;
4 o4 E0 ~8 E! Z) |+ Zs(1)=0;# r" \3 A* g9 l: u Q, ^8 Y7 |9 w
for t=2:N; , R& {) O$ f$ {2 s
p1(t)=a.^2*p(t-1)+Rww; / f/ G9 \5 b0 |' s
b(t)=c*p1(t)/(c.^2*p1(t)+Rvv); }$ H+ f5 c6 O4 u# K% B: @
s(t)=a*s(t-1)+b(t)*(Y(t)-a*c*s(t-1));
! }$ L7 _4 a$ l# u0 v tp(t)=p1(t)-c*b(t)*p1(t);
2 _3 z) X: ~& V e7 i( {. u" ]end
" m+ l+ Q& l& M+ ^9 O% Dt=1:N; , o0 X. H( V/ m1 T8 L$ q: P
plot(t,s,'r',t,Y,'g',t,x,'b'); 2 H. J$ G4 M6 V$ a, P. W, E2 l
function [x, V, VV, loglik] = kalman_filter(y, A, C, Q, R, init_x, init_V, varargin) ) x, m+ w- I g3 e" H/ c
% Kalman filter. ( ]8 }8 H4 B8 b6 M5 }7 F. Z
% [x, V, VV, loglik] = kalman_filter(y, A, C, Q, R, init_x, init_V, ...)
( C! w5 w U0 F) I: c%
; e y, I# J0 Z2 Z R X3 N% `% INPUTS: + q2 A2 U% ^! O" F0 J
% y(:,t) - the observation at time t
8 D8 h' c. i' H' p7 p* j8 B8 u' D% A - the system matrix " i$ E6 k+ Y# C* R/ B/ t
% C - the observation matrix
0 p' c2 K5 b d+ [0 J% K& h0 e! P& R% Q - the system covariance
4 u: z g) ^" J9 ` F% R - the observation covariance 5 X' {( W) r4 `9 {+ d* Y
% init_x - the initial state (column) vector
|! r& t# Z- R6 Y J2 i# B5 e% init_V - the initial state covariance 3 e t3 q9 O# g
%
) i( j* s4 f1 Y, a' g& v% OPTIONAL INPUTS (string/value pairs [default in brackets])
% Q2 n) F+ L9 f: P. {: Q8 i6 _% 'model' - model(t)=m means use params from model m at time t [ones(1,T) ] ) i( n; O/ d6 B6 V+ ?3 d x
% In this case, all the above matrices take an additional final dimension,
# m% {1 t$ W- P/ `: l7 i% i.e., A(:,:,m), C(:,:,m), Q(:,:,m), R(:,:,m). ' l/ O- K9 D" z4 q2 N
% However, init_x and init_V are independent of model(1). - C0 r" B* |; f: s# q! D4 [4 A5 c
% 'u' - u(:,t) the control signal at time t [ [] ] * G! p$ r9 d N: ~
% 'B' - B(:,:,m) the input regression matrix for model m 5 p2 m8 ~! y F+ y
%
, h" f$ p9 l6 v$ C9 ^) Z" v$ L% OUTPUTS (where X is the hidden state being estimated) / ?3 Q8 m8 p+ s4 i6 q* B
% x(:,t) = E[X(:,t) | y(:,1:t)]
" X3 X8 m8 j, w. M! b% V(:,:,t) = Cov[X(:,t) | y(:,1:t)]
3 U7 O! j+ G: J+ f% VV(:,:,t) = Cov[X(:,t), X(:,t-1) | y(:,1:t)] t >= 2 . Y- o. |# m; y* [' M
% loglik = sum{t=1}^T log P(y(:,t)) 4 Q, ]5 }% }) c4 ^4 K, {: v) ~
% * H% }. @" s0 t0 ?8 C
% If an input signal is specified, we also condition on it: 2 e0 k9 t, b7 D+ o
% e.g., x(:,t) = E[X(:,t) | y(:,1:t), u(:, 1:t)] 6 h4 v) {4 ~/ U! L% o
% If a model sequence is specified, we also condition on it: 7 `" P) w, D) r* g: H
% e.g., x(:,t) = E[X(:,t) | y(:,1:t), u(:, 1:t), m(1:t)]
$ ~3 u' x$ v- F9 ~* e/ C[os T] = size(y);
6 G9 t; ^0 }9 \1 Iss = size(A,1); % size of state space
9 A3 u- {1 M) c. ^6 y M, Y8 l) V% set default params
0 y- ` P$ L, ]+ f* p4 {9 P4 pmodel = ones(1,T);
3 G9 Z3 @2 s& t( v, Y- Qu = [];
7 ?% J7 }7 j, bB = [];
. u% W/ Y h0 z Wndx = []; 4 {- ^. {- z( N1 N0 U
args = varargin; 9 U% ]. |- n3 M! `% e
nargs = length(args);
7 O' \7 u# U9 ~- M( j) ]for i=1:2:nargs & x B9 O) q0 i0 f
switch args
' R# l! e& D; X+ ?; pcase 'model', model = args{i+1};
+ N( ?% Y, E' P8 Q9 H9 s! scase 'u', u = args{i+1};
# F9 I4 T+ \3 X& [% ]! F Acase 'B', B = args{i+1};
* o: a* W. `3 ocase 'ndx', ndx = args{i+1}; 1 v+ Q. }* v5 p
otherwise, error(['unrecognized argument ' args])
Q: @6 q3 s8 s6 W Q$ x y2 V: l7 Xend
) Y: h2 c. c5 Dend & l, P% b) W' {) V
x = zeros(ss, T); - e! |' Z/ b4 o- x; x2 r
V = zeros(ss, ss, T);
% T C, x% C2 s& S2 S# ~( r; WVV = zeros(ss, ss, T);
+ E( M2 `& o. Y# l, z) yloglik = 0; & K, v- E6 h, u: z7 J
for t=1:T m = model(t); ( f i3 M$ a5 I" {; ]" i! D2 B
if t==1 %prevx = init_x(:,m); ! r! e5 W6 F$ o |. }/ [
%prevV = init_V(:,:,m);
* Q% N8 o2 x: `prevx = init_x;
( k9 L( A$ p! Z! OprevV = init_V;
% K! n( _, j8 t( \7 o7 Xinitial = 1; ( [7 R# T7 e S& X) Y" Z
else prevx = x(:,t-1);
3 R3 x% r1 q. }# x4 w; T# D* oprevV = V(:,:,t-1); 0 d; {4 H$ i, }* M( ^3 o) p
initial = 0;
: z# Y0 L, m" S- \1 ~9 s+ M. \$ Aend 2 b- c: Z1 \ Q( P
if isempty(u) ' N$ B( [/ @% P& O( y
[x(:,t), V(:,:,t), LL, VV(:,:,t)] = ... 0 g4 n2 d6 b! C, S+ u B6 l( ~* q
kalman_update(A(:,:,m), C(:,:,m), Q(:,:,m), R(:,:,m), y(:,t), prevx, prevV, 'initial', initial); else ' f8 c1 C+ m% B: }# j
if isempty(ndx) [x(:,t), V(:,:,t), LL, VV(:,:,t)] = ...
6 C7 }2 m1 n0 T7 `, O" ]7 [% x kalman_update(A(:,:,m), C(:,:,m), Q(:,:,m), R(:,:,m), y(:,t), prevx, prevV, ... 'initial', initial, 'u', u(:,t), 'B', B(:,:,m));
6 b7 B; _4 |0 ?% E" yelse
0 D7 N( G6 G% ?6 Y* C; H: f, [) ]; fi = ndx; % H9 B9 M2 W! y6 K
% copy over all elements; only some will get updated x(:,t) = prevx;
* ?3 j) O/ y1 X" `prevP = inv(prevV);
3 b6 z$ ^+ U; C$ N! m" ZprevPsmall = prevP(i,i); % b$ l! {( T; e' P0 K$ j6 a
prevVsmall = inv(prevPsmall); ' N5 [+ L4 z. @2 C2 Q
[x(i,t), smallV, LL, VV(i,i,t)] = ... kalman_update(A(i,i,m), C(:,i,m), Q(i,i,m), R(:,:,m), y(:,t), prevx(i), prevVsmall, ... 'initial', initial, 'u', u(:,t), 'B', B(i,:,m));
! `' G' ~) l) {smallP = inv(smallV); ( C. Y8 ^. ] ?2 O; b$ X
prevP(i,i) = smallP; 0 \5 c; |3 m& e' z
V(:,:,t) = inv(prevP); 8 E5 j! `; N; h" ~) K
end * X# O" `8 k' p8 @. X3 a
end
& _( d' r* m. C: t% N: ploglik = loglik + LL;
8 S! Q! X" ]) [9 p2 |end |
|